Experiment 3

Prereaching infants’ understanding of reaching actions that cause state changes in objects on contact

Drawing inspiration from past studies of infants’ and adults’ causal perception (12, 13, 38, 39, 45), in Experiment 3 we tested infants’ responses to displays similar to those of Experiments 1 and 2, except that the person reached for and touched the ball, causing it to illuminate on contact, and then withdrew her hand, causing the ball to return to its initial state. To minimize the familiarity of both the action and the causal outcome while maximizing both the attractiveness of the state change event and the simplicity of the contact relation between the hand and the object, the actor reached with a gloved hand, as in Experiment 1, and she touched the object with the tips of her fingers, whereupon a light and soft sound activated within the ball for as long as the actor touched it (Figure 1, H3-H4, T3). Because this event has not been used in previous research, infants were randomly assigned to one of two habituation conditions (N=40; 20 per condition; Mean age=108 days; range=91-122, 23 female). In the experimental condition, infants watched the person reach over a barrier that prevented direct access to the goal object (H3), as in Experiments 1 and 2. In the control condition, infants watched the person perform the same reaches with the barrier behind the goal object, out of the actor’s way, as in the control condition of previous research with mitten-trained infants (H4) (29). Across both conditions, all barriers were added digitally to the same videos: Thus, the actor performed identical actions in the two conditions, but only in the first condition did the actor appear to reach efficiently on the habituation trials. After habituation, infants viewed the efficient, direct reach and the inefficient, indirect reach, as in Experiments 1-2, both of which activated the object (T3). These two conditions allow us to test whether infants differentiate efficient from inefficient reaches at test only when prior curved reaches were efficient.

In Experiment 3, infants responded differently to the test events across the two habituation conditions ([0.273,0.732], ß=0.781, B=0.502, SE=0.114, p<.001, two-tailed).When the actor’s reaches were initially constrained by a barrier (H1) in the experimental condition, infants looked longer, at test, at the inefficient than the efficient action (Mean_ineff=15.448s, Mean_eff=12.368s, [0.159,0.486], ß=0.501, B=0.322, SE=0.081, p<.001, two-tailed). Their preference for the inefficient test action cannot be attributed to low-level preferences for the curvilinear reach, because infants in the control condition (H2) showed a small preference in the opposite direction (Mean_ineff=8.788s, Mean_eff=10.104s, [-0.343,-0.017], ß=-0.28, B=-0.18, SE=0.081, p=0.032, two-tailed). ). Infants’ preference for the inefficient action was stronger in this experiment than in Experiment 1, which presented the same reaching trajectories ending in object pickup ([0.029,0.467], ß=0.457, B=0.248, SE=0.112, p=0.032, two-tailed). Experiment 3 therefore provides evidence that infants are sensitive to the physical constraints on object-directed reaching when these reaches terminate in a simple, causally transparent contact event.

Experiment 4

In Experiment 4, pre-registered at https://osf.io/a5byn/, we tested whether this sensitivity depends on infants’ construal of the actor as a causal agent who changes the states of objects on contact. We introduced digital manipulations to the habituation and test events from Experiment 3 to create a small spatial and temporal gap between the termination of the actor’s reach and the activation of the object, thereby removing the key condition that elicits causal perception in older infants and adults (12, 13, 38, 39, 45). Infants (N=20; Mean age=107 days; range=93-121; 12 female) saw videos identical to those from the experimental condition of Experiment 3, except the actor’s hand never contacted the object (her fingers paused 50 pixels, or 2 cm, above it), and the object changed state 0.5 seconds after the hand came to rest in midair (H5, T4). In contrast to Experiment 3, infants looked equally at test trials showing the inefficient and efficient actions (M_ineff=15.306s, M_eff=16.38s, [-0.301,0.191], ß=-0.096, B=-0.055, SE=0.119, p=0.649, two-tailed). Across Experiment 4 (H5, T4) and the experimental condition of Experiment 3 (H3, T3), infants responded differently to the test events depending on whether or not the person acted on the object on contact ([0.003,0.623], ß=0.547, B=0.313, SE=0.154, p=0.049, two-tailed). Therefore, Experiment 3 provides initial evidence that infants appreciate the physical constraints on goal-directed reaching if this action causes a change in its goal object on contact, but not if the change in the object occurs after, and at a distance from, the end of the action.

Experiment 5

To evaluate this suggestion further, we conducted a pre-registered direct replication of Experiments 3 and 4. In Experiment 5, pre-registered at https://osf.io/f2hvd/, we randomly assigned infants to events that differed only in spatiotemporal continuity: the object either activated on contact with the agent’s hand, or after a small gap in space and time (N=52, 26 per condition; Mean age=107 days; range=92-121; 21 female). This design allowed us to compare infants’ responses to causal (H3, T3) versus non-causal (H5, T4) actions, under testing conditions where all researchers were blind to condition as well as test events. We fully replicated the findings from Experiments 3 and 4: Infants again responded to the test events differently depending on whether or not the activation of the object occurred on contact with the hand ([0.184,0.815], ß=0.729, B=0.5, SE=0.158, p=0.003, two-tailed). As in Experiment 3, infants looked longer at the inefficient than the efficient reach when the person appeared to cause a change in the object (M_ineff=12.166s, M_eff=7.791s, [0.211,0.66], ß=0.635, B=0.435, SE=0.112, p<.001, one-tailed); as in Experiment 4, infants looked equally to the inefficient and efficient reaches when she did not appear to cause this outcome(M_ineff=11.395s, M_eff=12.888s, [-0.289,0.16], ß=-0.094, B=-0.064, SE=0.112, p=0.567, two-tailed). Although 3-month-old infants have limited experience acting on objects themselves, they understand that other people intend to cause changes in the world through their actions. Infants exhibited this ability in Experiments 3 and 5, both of which presented clear information that a change in the goal object occurred on contact with the actor’s hand.

Comparing results including and excluding influential participants.

Across all of our experiments, we checked for influential participants in every model using Cook’s Distance (69), as stated in the main text. This is a method for outlier detection: The purpose of this step in our analysis is to identify individuals whose inclusion in the analysis may have undue influence by either masking the effect, which is otherwise present across the rest of the sample, or by driving the effect, which is otherwise absent across the rest of the sample. Below are the results from the main text detailing how many influential participants were detected in each analysis, and report the results including these participants. Overall, none of the main conclusions reported in the main text differ depending on the inclusion or exclusion of these participants (though see below for a minor difference in the findings from Experiment 2, and the analysis collapsing across Experiment 1 and Skerry et al. (2013)).

In the primary analysis for Experiment 1, we detected one influential participant. Including this participant in the analysis generates the same finding as reported in the main text: Infants looked equally at the efficient vs inefficient reach of a gloved hand ([-0.169,0.209], ß=0.041, B=0.02, SE=0.092, p=0.831, two-tailed). In the analysis comparing Experiment 1 to Skerry et al. (2013) Experiment 3, we detected 2 influential participants. Including them results in a null difference between these two experiments ([-0.086,0.415], ß=0.279, B=0.165, SE=0.128, p=0.205, two-tailed). This difference does not change our interpretation of Experiment 1: Infants do not appear to respond to the efficiency of pickup actions when the person reaching wears a glove or a mitten.

In the primary analysis for Experiment 2, we detected 2 influential participants. Including them in the sample generates a marginal effect in the same direction as that reported in the main text: Infants looked longer at the inefficient than the efficient reach of a bare hand ([-0.024,0.318], ß=0.297, B=0.147, SE=0.083, p=0.091, two-tailed). In the analysis comparing Experiment 2 to Skerry et al. (2013) Experiment 3, we detected 1 influential participant. Including them results in the same finding as reported in the main text: Infants’ looking preferences significantly differed across these two experiments ([0.048,0.536], ß=0.495, B=0.292, SE=0.121, p=0.021, two-tailed). These findings do not change our conclusion in the main text: Experiments 1 and 2 overall show that infants have inconsistent, fragile expectations about the efficiency of reaches that result in displacing objects.

In the analysis collapsing across Experiments 1 and 2, we found 1 influential participant. Inclusion of that participant generates a null effect ([-0.042,0.209], ß=0.139, B=0.083, SE=0.063, p=0.191, two-tailed), whereas in the main text this effect was marginal, but our conclusion is the same: Infants do not show robust sensitivity to the cost of reaching actions when these actions result in objects being displaced. In the analysis comparing infants’ looking preferences across Experiments 1 and 2, we found 3 influential participants, and including them results in the same result as reported in the main text: Infants’ looking preferences did not differ across the two experiments, ([-0.116,0.37], ß=0.211, B=0.127, SE=0.124, p=0.311, two-tailed).

In the primary analysis for Experiment 3, we detected 2 influential participants. Including them in the sample generates the same finding as reported in the main text: Infants’ looking preferences for the test events differed as a function of whether they were habituated to constrained action over a barrier (experimental group) or the same actions not over a barrier (control group) ([0.115,0.657], ß=0.596, B=0.502, SE=0.114, p<.001, two-tailed). In the experimental condition, infants looked longer at the inefficient action ([0.065,0.451], ß=0.398, B=0.258, SE=0.095, p=0.01, two-tailed). In the control condition, infants looked equally at the two test actions ([-0.321,0.065], ß=-0.198, B=-0.128, SE=0.095, p=0.186, two-tailed).

We did not detect any influential participants in the analyses for Experiments 4 and 5.

Comparing bare hands, gloves, and mittens

Because Experiments 1 and 2 used the methods of Skerry et al. (2013), the primary difference between the events from Skerry et al. (2013) (SCS), and Experiments 1 and 2 from the main text concerned the presentation of the reaching hand, which was bare in Experiment 2, covered by tight-fitting gloves in Experiment 1, and covered by thick mittens in SCS, as in all the prior published research involving mittens training. Could infants’ responses to the reaches from these experiments be explained, in part, by how easy it was to see the configuration of the hand (easy in Experiment 2, slightly harder in Experiment 1, and even harder in SCS)? To explore this question, we analyzed infants’ proportion looking to the inefficient action in Experiment 1, Experiment 2, and the comparable experiment from SCS where infants had no mittens training (SCS Experiment 3), and asked whether the clarity of the person’s hand in each of these experiments (2 in Experiment 2, 1 in Experiment 1, and 0 in SCS Experiment 3) predicted differences in looking preferences, controlling for correlated data within experiments. This analysis revealed that infants’ sensitivity to the efficiency of this reach increased with increasingly clear information about the form of the hand ([0.007,0.053], ß=0.416, B=0.03, SE=0.011, p=0.011, two-tailed, excluding 4 influential participants). This finding held regardless of whether the influential participants were excluded or included (in the latter case, [0.005,0.053], ß=0.359, B=0.029, SE=0.012, p=0.02, two-tailed). ## Meta-analytic results

To assess the effects of our experimental manipulations in Experiments 1-5 and in Skerry et al. (29), we performed an analysis over these two papers (total N=264, 12 conditions). Our analytic approach allows us to assess the independent effects of 5 manipulations: the type of or absence of motor training, the presence or absence of a barrier preventing a direct reach for the object during habituation, the nature of the goal (to change the state of an object or pick it up), the presence or absence of action on contact, and the presence or absence of mittens on the actor. The analysis also allows us to control for the participant variables of age and sex, and model the nested structure of the data (e.g. looks clustered within experiments and within papers). For ease of interpretation, we used average proportion looking to the inefficient action in this analysis, following Skerry et al. (29). The findings below exclude 16 participants on the basis of Cook’s Distance, leaving 248 infants in the final sample. See Table S1 for results including all participants.

This analysis confirmed the findings from the individual experiments reported in the main text and in Skerry et al. (28): Infants’ expectations were stronger when the observed action was spatiotemporally continuous with its effect (i.e., appeared to be causal), [0.025,0.058], ß=0.467, B=0.041, SE=0.009, p<.001, two-tailed, when infants received effective motor training (sticky mittens), relative to no training [0.029,0.074], ß=0.583, B=0.052, SE=0.011, p<.001, two-tailed, when the observed agent’s actions were constrained by a barrier and were efficiently adapted to that barrier, relative to the same actions that were unconstrained by a barrier, [0.021,0.051], ß=0.406, B=0.036, SE=0.008, p<.001, two-tailed, and when the agent pursued a state change goal, relative to a pickup goal, [0.011,0.042], ß=0.302, B=0.027, SE=0.008, p=0.001, two-tailed. We also found that infants’ expectations were marginally negatively affected when they received ineffective motor training (non-sticky mittens), relative to no training, [-0.058,0], ß=-0.33, B=-0.029, SE=0.015, p=0.051, two-tailed, and improved as the form of the hand became clearer [0.003,0.056], ß=0.333, B=0.03, SE=0.013, p=0.027, two-tailed, but neither of the latter two findings was present in the full analysis with all participants (see Table S1). These findings provide further evidence that action experience alters action interpretation, but so does causal information and information about efficiency.

Table S1. (A) Regression table for model investigating predictors of sensitivity to action efficiency across Experiment 1-5 and all experiments from Skerry et al. (29) (total N=264, 248 included in final analysis, 16 excluded on the basis of Cook’s Distance). (B) Regression table for the same analysis, including all participants. Dependent measure is proportion looking towards the inefficient reach, averaged across 3 test trials during test. Categorical predictors were coded using sum contrasts, and fixed effects from the model should therefore be interpreted with respect to the grand mean. Model formula prop.ineff.all ~ training + goal + hab + causal + mitten + (1|experiment) + (1|ageday) + (1|sex) + (1|paper).

Exclusion info

Table S2. Tally of infants who participated in Experiments 1-5 but were excluded in our final sample. These exclusion criteria vary slightly across experiments (e.g. we relaxed our definition of inattentiveness from excluding all data from a participant if they missed a test trial in Experiment 1, to excluding data from just that trial in Experiments 2-5).

Distribution of Looks

Figure S3. Density plot of looking times during test across Experiments 1-5 from the present research (Liu, Brooks, and Spelke; LBS, left panel), and Experiments 1-5 from Skerry et al. (2013) (SCS, right panel) (N=264). Maximum-likelihood fitting revealed that the lognormal distribution (log likelihood=-1720.509) provides a better fit to these data than the normal distribution (log likelihood=-1842.196).

Attention during habituation across Exp 1-5

Figure S4. Total looking time in seconds during habituation across Experiments 1-5. Error bars around means indicate bootstrapped 95% confidence intervals (CIs). Individual points indicate data from a single participant. Horizontal bars within boxes indicate medians, and boxes indicate the middle 2 quartiles of data. Violin plots in indicate distribution of data, area scaled proportionally to the number of observations.

To ask whether infants’ total attention during habituation was affected by experimental manipulations across Experiments 1-5 (action constrained vs unconstrained by a barrier, state change vs pickup goal, mittened, gloved, or bare-handed actor, and action with vs without contact with the object), and varied by gender and age, we fit a mixed effects model on these fixed effects and experiment (1-5) as a random intercept. We found that the only robust predictor of attention during habituation was age, [-3.4,-0.714], ß=-0.233, B=-2.058, SE=0.68, p=0.003, two-tailed, such that older infants looked for a shorter time overall than younger infants.

Table S3 Regression table for mixed effects model analyzing the effect of age, sex, order of test events, habituation condition, goal, coverage of the hand, and causal information on total looking time habituation, controlling for other variations across Experiments 1-5. Model formula: total_hab ~ ageday + sex + first.test + hab + goal + clarity + causal + (1|experiment).